Abstract
We present a numerical method for the solution of integro-differential equations describing motion of an incompressible viscoelastic fluid with memory. In particular, the system of equations consists of the momentum conservation equation with the Cauchy stress tensor divided in a viscous and an elastic parts which depend non-linearly on the symmetric part of velocity gradient and non-linearly on the past values of the Finger strain tensor, respectively. The momentum conservation equation is completed with system of equations that describes relation between the velocity gradient and the Finger strain tensor. The method is based on a discontinuous Galerkin method in the spatial variables and the BDF methods in the time variables.
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Acknowledgements
This work was supported by the Grant No. 454213 of the Grant Agency of the Charles University.
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Soukup, I. (2016). Numerical Method Based on DGM for Solving the System of Equations Describing Motion of Viscoelastic Fluid with Memory. In: Karasözen, B., Manguoğlu, M., Tezer-Sezgin, M., Göktepe, S., Uğur, Ö. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2015. Lecture Notes in Computational Science and Engineering, vol 112. Springer, Cham. https://doi.org/10.1007/978-3-319-39929-4_21
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DOI: https://doi.org/10.1007/978-3-319-39929-4_21
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